Simplify the following expression: $\dfrac{40y^3}{96y^3}$ You can assume $y \neq 0$.
$ \dfrac{40y^3}{96y^3} = \dfrac{40}{96} \cdot \dfrac{y^3}{y^3} $ To simplify $\frac{40}{96}$ , find the greatest common factor (GCD) of $40$ and $96$ $40 = 2 \cdot 2 \cdot 2 \cdot 5$ $96 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3$ $ \mbox{GCD}(40, 96) = 2 \cdot 2 \cdot 2 = 8 $ $ \dfrac{40}{96} \cdot \dfrac{y^3}{y^3} = \dfrac{8 \cdot 5}{8 \cdot 12} \cdot \dfrac{y^3}{y^3} $ $\phantom{ \dfrac{40}{96} \cdot \dfrac{3}{3}} = \dfrac{5}{12} \cdot \dfrac{y^3}{y^3} $ $ \dfrac{y^3}{y^3} = \dfrac{y \cdot y \cdot y}{y \cdot y \cdot y} = 1 $ $ \dfrac{5}{12} \cdot 1 = \dfrac{5}{12} $